In the 2nd Temple Era, there existed a sect of Jews known as the Sadducees (named after their leader, Saddok). This misguided sect denied the Divine origin of the Oral Law, and lived their lives by their own interpretation of the Scriptures.
One of their misinterpretations of the Scriptures concerned cooking on the Shabbat. The Torah says, "You shall not kindle fire in any of your dwelling places on the Sabbath day" (Exodus 35:3). The Sadducees understood this verse as a prohibition against having a fire burning on the Shabbat. Therefore, every Shabbat they would sit in the cold and darkness, and would eat only cold food.
In truth, the Torah only forbids the act of kindling a fire on Shabbat -- it does not prohibit having on Shabbat a flame which was ignited beforehand.
The Pharisees -- literally: the "separationists," the Jews who remained loyal to the Rabbinic Torah and separated themselves from the errant Sadducees -- demonstrated their allegiance to the Oral Law by making a point of eating a hot dish on Shabbat afternoon.
In fact, many argue that the word "Cholent" comes from the Hebrew word "Shelahn," which means that it "rested overnight" on the fire.
Aside for the technical reasons for eating Cholent, we also must note that it is a tasty dish (which in itself is a good reason for the custom), and there's nothing like a Shabbat afternoon nap which follows a plate of